AEI–DFG: Optimization over Nonlinear Model Spaces: Where Discrete Meets Continuous Optimization

• Applicants: Professor Dr. David Russell Luke; Professor Dr. Stefan Nickel
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 541767835

The overarching goal of this research project is to bring the experience and understanding from discrete and continuous optimization together under a single, albeit broad optimization model, enabling the transfer of advances for particular contexts and problem instances to other areas via the relationship to one unifying abstract template. This central problem linking the subprojects is the Ordered Median of Polynomial Functions problem. In the following we will name the most important general objectives of this proposal. We will give in addition the specific (more technical) objectives of each of the eight work packages. The general goals of this proposal are: • To improve the interplay and the synergy between continuous and discrete optimization problems – and to see if some unified mathematical tools can be identified. • To expand the theoretical understanding of structural properties of optimization problems, both discrete and continuous, to nonlinear model spaces. • To develop new model descriptions and improved algorithms using these new model descriptions. This is motivated by the fact that in the ordered median modeling context we are able to express min-sum and min-max problems in a unified way. • To develop better exact and heuristic solution methodologies for concrete optimization problems using the results of the above objectives. • To establish a series of common workshops for improving the collaboration between the participating teams as well as a better understanding between the discrete on continuous mathematical community.

• DFG Programme: Research Grants
• International Connection: Spain
• Partner Organisation: Agencia Estatal de Investigación
• Co-Investigator: Professor Dr. Oliver Stein
• Cooperation Partners: Professor Dr. Justo Puerto; Professor Dr. Juan Jose Salazar Gonzalez